Theoretical Population Biology最新文献_第2页

Computing tree size under dynamical models of diversification 动态多样化模型下的树大小计算。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-10-27 DOI: 10.1016/j.tpb.2025.10.003

Ailene MacPherson , Matt Pennell

A phylogenetic tree has three types of attributes: size, shape (topology), and branch density. Phylodynamic studies are often motivated by questions regarding the size of clades, nevertheless, nearly all of the inference methods only make use of the other two attributes. In this paper, we ask whether there is additional information if we consider tree size more explicitly in phylodynamic inference methods. To address this question, we first needed to be able to compute the expected tree size distribution under a specified phylodynamic model; perhaps surprisingly, there is not a general method for doing so — it is known what this is under a Yule or constant rate birth–death model but not for the more complicated scenarios researchers are often interested in. We present three different solutions to this problem: using (i) the deterministic limit; (ii) master equations; and (iii) an ensemble moment approximation. Using simulations, we evaluate the accuracy of these three approaches under a variety of scenarios and alternative measures of tree size (i.e., sampling through time or only at the present; sampling ancestors or not). We then use the most accurate measures for the situation, to investigate the added informational content of tree size. We find that for two critical phylodynamic questions — (i) is diversification diversity dependent? and, (ii) can we distinguish between alternative diversification scenarios? — knowing the expected tree size distribution under the specified scenario provides insights that could not be gleaned from considering the expected shape and branch density alone. The contribution of this paper is both a novel set of methods for computing tree size distributions and a path forward for richer phylodynamic inference into the evolutionary and epidemiological processes that shape lineage trees.

系统发育树有三种类型的属性：大小、形状（拓扑结构）和分支密度。系统动力学研究经常被有关枝的大小的问题所激发，然而，几乎所有的推理方法都只利用了其他两个属性。在本文中，我们问是否有额外的信息，如果我们考虑树的大小更明确地在系统动力学推理方法。为了解决这个问题，我们首先需要能够在特定的系统动力学模型下计算预期的树大小分布；也许令人惊讶的是，没有一个通用的方法来做到这一点——在Yule或恒定速率的出生-死亡模型下，这是已知的，但对于研究人员经常感兴趣的更复杂的情况，这是未知的。我们对这个问题提出了三种不同的解决方案：使用(i)确定性极限；（ii）主方程；和（iii）一个集合矩近似。通过模拟，我们评估了这三种方法在各种场景和树大小的替代测量下的准确性（即，随时间采样或仅在当前采样；采样祖先与否）。然后，我们使用最准确的测量方法来调查树大小的附加信息内容。我们发现，对于两个关键的系统动力学问题——(i)多样化是否依赖于多样性？（ii）我们能否区分不同的多样化方案？-了解在特定情况下预期的树木大小分布，可以提供仅考虑预期形状和树枝密度无法获得的见解。本文的贡献在于提供了一套计算树大小分布的新方法，并为形成谱系树的进化和流行病学过程提供了更丰富的系统动力学推断。

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引用次数: 0

Consistency and central limit results for the maximum likelihood estimator in the Admixture Model 混合模型中最大似然估计量的一致性和中心极限结果

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-10-08 DOI: 10.1016/j.tpb.2025.10.001

Carola Sophia Heinzel

In the Admixture Model, the probability of an individual having a certain number of alleles at a specific marker depends on the allele frequencies in

K

ancestral populations and the fraction of the individual’s genome originating from these ancestral populations.

This study investigates consistency and central limit results of maximum likelihood estimators (MLEs) for the ancestry and the allele frequencies in the Admixture Model, complimenting previous work by Pfaff et al. (2004); Pfaffelhuber and Rohde (2022). Specifically, we prove consistency of the MLE, if we estimate the allele frequencies and the ancestries. Furthermore, we prove central limit theorems, if we estimate the ancestry of a finite number of individuals and the allele frequencies of finitely many markers, also addressing the case where the true ancestry lies on the boundary of the parameter space.

Finally, we use the new theory to quantify the uncertainty of the MLEs for the data of the 1000 Genomes Project.

在混合模型中，个体在特定标记上具有一定数量等位基因的概率取决于K个祖先群体中的等位基因频率和个体基因组中来自这些祖先群体的部分。本研究调查了混合模型中祖先和等位基因频率的最大似然估计（MLEs）的一致性和中心极限结果，补充了Pfaff等人（2004）的先前工作；Pfaffelhuber and Rohde（2022）。具体来说，如果我们估计等位基因频率和祖先，我们证明了MLE的一致性。此外，我们证明了中心极限定理，如果我们估计有限个个体的祖先和有限个标记的等位基因频率，也解决了真正的祖先位于参数空间边界的情况。最后，我们利用新理论量化了千人基因组计划数据的mle的不确定性。

引用次数: 0

Inconsistency of parsimony under the multispecies coalescent 多种合并下节俭的不一致性。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-09-27 DOI: 10.1016/j.tpb.2025.09.004

Daniel A. Rickert , Louis Wai-Tong Fan , Matthew W. Hahn

While it is known that parsimony can be statistically inconsistent under certain models of evolution due to high levels of homoplasy, the consistency of parsimony under the multispecies coalescent (MSC) is less well studied. Previous studies have shown the consistency of concatenated parsimony (parsimony applied to concatenated alignments) under the MSC for the rooted 4-taxa case under an infinite-sites model of mutation; on the other hand, other work has also established the inconsistency of concatenated parsimony for the unrooted 6-taxa case. These seemingly contradictory results suggest that concatenated parsimony may fail to be consistent for trees with more than 5 taxa, for all unrooted trees, or for some combination of the two. Here, we present a technique for computing the expected internal branch lengths of gene trees under the MSC. This technique allows us to determine the regions of the parameter space of the species tree under which concatenated parsimony fails for different numbers of taxa, for rooted or unrooted trees. We use our new approach to demonstrate that while parsimony succeeds in the unrooted 5-taxa case, there are regions of statistical inconsistency for concatenated parsimony for rooted 5+-taxa cases and unrooted 6+-taxa cases. Our results therefore suggest that parsimony is not generally dependable under the MSC.

虽然我们知道，在某些进化模式下，由于高水平的同源性，简约性可能在统计上不一致，但对多物种聚结（MSC）下简约性的一致性研究较少。先前的研究表明，在无限位点突变模型下，MSC下的4个根分类群的串联简约性（应用于串联比对的简约性）的一致性；另一方面，其他研究也证实了6个分类群无根情况下串联简约性的不一致性。这些看似矛盾的结果表明，串联简约可能不符合5个以上分类群的树木、所有无根树木或两者的某些组合。在这里，我们提出了一种计算MSC下基因树的预期内部分支长度的技术。这种技术使我们能够确定物种树的参数空间的区域，在该区域内，对于不同数量的分类群，对于有根或无根的树，串联简约性失败。我们使用我们的新方法来证明，虽然在无根的5-分类群情况下简约性成功，但在有根的5+-分类群情况下和无根的6+-分类群情况下，串联简约性存在统计不一致的区域。因此，我们的结果表明，在MSC下，节俭通常是不可靠的。

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引用次数: 0

Dynamics of the distribution of fitness effects during adaptation 适应度效应在适应过程中的动态分布。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-09-22 DOI: 10.1016/j.tpb.2025.09.003

Tenoch Morales, Abigail Kushnir, Lindi M. Wahl

Empirical measures of the distribution of fitness effects of new mutations (the DFE) have been increasingly successful, and have recently highlighted the fact that the DFE changes during adaptation. Here, we analyze these dynamic changes to the DFE during a simplified adaptive process: an adaptive walk across an additive fitness landscape. First, we derive analytical approximations for the underlying fitness distributions of alleles present in the genotype and available through mutation and use these to derive expressions for the DFE at each step of the adaptive walk. We then confirm these predictions with independent simulations that relax several simplifying assumptions made in the analysis. As expected, our analysis predicts that as adaptation proceeds, the DFE is reshaped dynamically throughout the walk by a decrease in the beneficial fraction of mutations (a shift to the left). Surprisingly, different mechanisms drive this change depending on the number of alleles available per site: for a small number of available alleles, we observe a depletion of high-fitness alleles available through mutation as expected, however for a large number of alleles we observe that adaptation may be more limited by the availability of low-fitness alleles to be replaced, rather than by the availability of high-fitness alleles to replace them.

新突变适应度效应分布（DFE）的实证测量越来越成功，最近强调了DFE在适应过程中发生变化的事实。在这里，我们分析了在一个简化的适应过程中DFE的这些动态变化：在一个附加适应度景观上的自适应行走。首先，我们推导出基因型中存在的等位基因的潜在适应度分布的分析近似，并通过突变获得，并使用这些近似来推导出适应行走每一步的DFE的表达。然后，我们用独立的模拟来证实这些预测，这些模拟放松了分析中做出的几个简化假设。正如预期的那样，我们的分析预测，随着适应的进行，DFE在整个行走过程中通过有益突变比例的减少（向左移动）动态重塑。令人惊讶的是，不同的机制驱动这种变化取决于每个位点可用的等位基因的数量：对于少数可用的等位基因，我们观察到预期的高适应度等位基因通过突变耗尽，然而对于大量的等位基因，我们观察到适应可能更多地受到低适应度等位基因替代的可用性的限制，而不是高适应度等位基因替代它们的可用性。

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引用次数: 0

An equal-tempered measure of linkage disequilibrium 连杆不平衡的一种均匀测量。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-09-12 DOI: 10.1016/j.tpb.2025.09.002

Mark M. Tanaka

Linkage disequilibrium (LD), the association of alleles at two loci, is defined in multiple ways. Because LD measures depend on allele frequencies, it is difficult to compare LD values between populations or loci with different allele frequencies. Here, I consider a geometric interpretation of a commonly used LD measure

r^{2}

which suggests a modification that is frequency-independent in the sense that equal evolutionary forces lead to the same effect at different frequencies. This new measure is a very simple expression that is known elsewhere as the Hamann coefficient and the G index of agreement; it is a linear transformation of the simple matching coefficient. I explore properties of this quantity in comparison with

D

and

r^{2}

, and discuss its interpretation, advantages and disadvantages.

连锁不平衡（LD），等位基因在两个位点的关联，有多种定义。由于LD测量依赖于等位基因频率，因此很难比较具有不同等位基因频率的种群或位点之间的LD值。在这里，我考虑了常用的LD测量r2的几何解释，它表明了一种频率无关的修改，即相等的进化力在不同频率上导致相同的效果。这个新度量是一个非常简单的表达式，在其他地方被称为哈曼系数和G一致指数；它是简单匹配系数的线性变换。通过与D和r2的比较，探讨了这个量的性质，并讨论了它的解释和优缺点。

引用次数: 0

Tikhonov–Fenichel reductions and their application to a novel modelling approach for mutualism Tikhonov-Fenichel约简及其在互惠共生新建模方法中的应用。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-09-11 DOI: 10.1016/j.tpb.2025.08.004

Johannes Apelt, Volkmar Liebscher

When formulating a model there is a trade-off between model complexity and (biological) realism. In the present paper we demonstrate how model reduction from a precise mechanistic “super model” to simpler conceptual models using Tikhonov–Fenichel reductions, an algebraic approach to singular perturbation theory, can mitigate this problem. Compared to traditional methods for time scale separations (Tikhonov’s theorem, quasi-steady state assumption), Tikhonov–Fenichel reductions have the advantage that we can compute a reduction directly for a separation of rates into slow and fast ones instead of a separation of components of the system. Moreover, we can find all such reductions algorithmically.

In this work we use Tikhonov–Fenichel reductions to analyse a mutualism model tailored towards lichens with an explicit description of the interaction. We find: (1) the implicit description of the interaction given in the reductions by interaction terms (functional responses) varies depending on the scenario, (2) there is a tendency for the mycobiont, an obligate mutualist, to always benefit from the interaction while it can be detrimental for the photobiont, a facultative mutualist, depending on the parameters, (3) our model is capable of describing the shift from mutualism to parasitism, (4) via numerical analyis, that our model experiences bistability with multiple stable fixed points in the interior of the first orthant. To analyse the reductions we formalize and discuss a mathematical criterion that categorizes two-species interactions. Throughout the paper we focus on the relation between the mathematics behind Tikhonov–Fenichel reductions and their biological interpretation.

在制定模型时，需要在模型复杂性和（生物）现实性之间进行权衡。在本文中，我们展示了如何使用奇异微扰理论的代数方法Tikhonov-Fenichel约简，从一个精确的机械“超级模型”到更简单的概念模型，可以缓解这个问题。与传统的时间尺度分离方法（Tikhonov定理，准稳态假设）相比，Tikhonov- fenichel约简的优点是，我们可以直接计算速率分离为慢速和快速的约简，而不是系统组件的分离。此外，我们可以通过算法找到所有这些约简。在本文中，我们使用Tikhonov-Fenichel约简来分析一个针对地衣的互惠模式，并明确描述了这种相互作用。我们发现:(1)通过相互作用项（功能响应）在减少中给出的相互作用的隐式描述因情景而异；(2)根据参数，真菌生物（义务互惠者）总是从相互作用中受益，而光生物（兼性互惠者）则可能有害；(3)我们的模型能够描述从互惠到寄生的转变；(4)通过数值分析。我们的模型具有双稳定性，在第一正交内具有多个稳定不动点。为了分析约简，我们形式化并讨论了对两种相互作用进行分类的数学标准。在整个论文中，我们关注的是吉洪诺夫-菲尼切尔约化背后的数学与它们的生物学解释之间的关系。

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引用次数: 0

The Feller diffusion conditioned on a single ancestral founder 费勒扩散以一个单一的祖先奠基人为条件。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-09-10 DOI: 10.1016/j.tpb.2025.09.001

Conrad J. Burden , Robert C. Griffiths

We examine the distributional properties of a Feller diffusion

{(X (τ))}_{τ \in [0, t]}

conditioned on the current population

X (t)

having a single ancestor at time zero. The approach is novel and is based on an interpretation of Feller’s original solution according to which the current population is comprised of a Poisson number of exponentially distributed families, each descended from a single ancestor. The distribution of the number of ancestors at intermediate times and the joint density of coalescent times is determined under assumptions of initiation of the process from a single ancestor at a specified time in the past, including infinitely far in the past, and for the case of a uniform prior on the time since initiation. Also calculated are the joint distribution of the time since the most recent common ancestor of the current population and the contemporaneous population size at that time under different assumptions on the time since initiation. In each case exact solutions are given for supercritical, critical and subcritical diffusions. For supercritical diffusions asymptotic forms of distributions are also given in the limit of unbounded exponential growth.

我们研究了Feller扩散(X(τ))τ∈[0，t]的分布特性，条件是当前种群X(t)在时间0时具有单一祖先。该方法是新颖的，基于Feller原始解决方案的解释，根据该解决方案，当前种群由指数分布的家族的泊松数组成，每个家族都来自单个祖先。中间时间的祖先数量分布和接合时间的联合密度是在以下假设下确定的：在过去的特定时间，包括无限远的过去，从一个单一的祖先开始这个过程，以及在开始后的时间有一个均匀的先验。还计算了当前种群从最近的共同祖先开始的时间的联合分布，以及当时在不同假设下的同期种群规模。在每种情况下，都给出了超临界、临界和亚临界扩散的精确解。对于超临界扩散，给出了无界指数增长极限下分布的渐近形式。

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引用次数: 0

The distribution of the number of mutations in the genealogy of a sample from a single population 突变数：来自单一种群的一个样本的家谱中突变数的分布

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-08-26 DOI: 10.1016/j.tpb.2025.08.001

Yun-Xin Fu

The number

K

of mutations in the genealogy of a sample of

n

sequences from a single population is one essential summary statistic in molecular population genetics and is equal to the number of segregating sites in the sample under the infinite-sites model. Although its expectation and variance are the most widely utilized properties, its sampling formula (i.e., probability distribution) is the foundation for all explorations related to K. Despite existence of an analytic sampling formula, its numerical application is limited due to susceptibility to error propagation. This paper presents a new sampling formula for

K

in a random sample of DNA sequences from a neutral locus without recombination, taken from a single population evolving according to the Wright–Fisher model with a constant effective population size, or the constant-in-state model, which allows the effective population size to vary across different coalescent states. The new sampling formula is expressed as the sum of the probabilities of the various ways mutations can manifest in the sample genealogy and achieves simplicity by partitioning mutations into hypothetical atomic clusters that cannot be further divided. Under the Wright–Fisher model with a constant effective population size, the new sampling formula is closely analogous to the celebrated Ewens’ sampling formula for the number of distinct alleles in a sample. Numerical computation using the new sampling formula is accurate and is limited only by the burden of enumerating a large number of partitions of a large K. However, significant improvement in efficiency can be achieved by prioritizing the enumeration of partitions with a large number of parts.

在分子群体遗传学中，单个群体的n个序列样本的家谱突变数K是一个重要的汇总统计量，在无限位点模型下等于样本中的分离位点数。虽然它的期望和方差是最广泛使用的性质，但它的抽样公式（即概率分布）是所有与k相关的探索的基础。尽管存在解析抽样公式，但由于易受误差传播的影响，其数值应用受到限制。根据Wright-Fisher模型（有效群体规模恒定）或恒态模型（允许有效群体规模在不同的聚合状态下变化），从一个无重组的中性位点DNA序列的随机样本中，提出了一个新的K抽样公式。新的抽样公式表示为突变在样本谱系中表现的各种方式的概率之和，并通过将突变划分为不能进一步划分的假想原子簇来实现简单性。在有效群体大小不变的Wright-Fisher模型下，新的抽样公式与著名的evens样本中不同等位基因数量的抽样公式非常相似。使用新抽样公式的数值计算是准确的，并且仅受枚举大k的大量分区的负担的限制。然而，通过优先枚举具有大量零件的分区可以显着提高效率。

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引用次数: 0

Gene-culture association and coevolution 基因-文化关联与共同进化

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-08-23 DOI: 10.1016/j.tpb.2025.08.003

Laurel Fogarty , Stephen Zhang , Marcus W. Feldman

The genetic evolution of cultural species can be altered by the dynamic interaction of their genes with their cultural traits. In humans, examples of gene-culture interactions are common and a deeper theoretical understanding of gene-culture coevolution is a necessary precursor to recognizing the effects of culture on human evolution. Although there are a large number of empirical studies of gene-culture coevolutionary phenomena and a large amount of verbal theory, our theoretical understanding of gene-culture co-evolution, of what kinds of cultural traits are relevant, and of the quantitative nature of cultural interactions with genes remains incomplete. Two models of gene-culture coevolution in which there are interactions between cultural transmission biases, viability selection, and genetic evolution are presented. We show that gene-culture coevolution can occur in the absence of selection on the cultural trait, that some parameters can lead to internal equilibria in which all genetic and cultural types are polymorphic, that gene-culture association may be maintained, and that gene-culture coevolutionary systems have rich and unexpected dynamics.

文化物种的遗传进化可以通过其基因与其文化性状的动态相互作用而改变。在人类中，基因-文化相互作用的例子是常见的，对基因-文化共同进化的更深入的理论理解是认识文化对人类进化影响的必要前提。尽管有大量关于基因-文化共同进化现象的实证研究和大量的语言理论，但我们对基因-文化共同进化的理论理解，哪些文化特征是相关的，以及文化与基因相互作用的定量性质仍然不完整。提出了文化传播偏差、生存力选择和遗传进化三者之间相互作用的两种基因-文化协同进化模型。我们表明，基因-文化共同进化可以在没有文化特征选择的情况下发生，一些参数可以导致所有遗传和文化类型都是多态的内部平衡，基因-文化关联可以保持，基因-文化共同进化系统具有丰富和意想不到的动态。

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引用次数: 0

Prevalence of social parasitism in ant populations: Modeling energetics, demography and space in the Polyergus/Formica system 蚁群中社会寄生性的流行：Polyergus/Formica系统的能量学、人口学和空间建模。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-08-11 DOI: 10.1016/j.tpb.2025.08.002

Patrick J. Talley , Frederick R. Adler

Obligatory interspecific brood raiding is a unique form of parasitism in which one ant species steals pupae from another species and raises them into workers to perform duties within its nest. Although this strategy can support very large colonies, the relative species abundance of these social parasites is always low. Using fully parameterized mathematical models of the growth and reproduction of the well-studied interaction between brood raider Polyergus and its hosts in the genus Formica, we aim to discover the mechanisms that limit brood raider abundance. These mathematical models explain the range of observed relative species abundance of these social parasites and provide a criterion for Polyergus persistence within a patch of hosts. In particular, Polyergus colony survival depends on the number of host colonies between 23 and 73 meters from their nest—close enough to raid but distant enough to survive raiding. The number sets the upper bound of Polyergus abundance to be less than 10% of the community. Furthermore, we quantify the fitness costs imposed by brood raiding on nearby host colonies, which can be effectively castrated by the constant drain on their worker resources. These findings provide a mechanistic framework for understanding the ecological constraints on social parasitism, its role in shaping ant community dynamics and its connection to the evolution of host defense strategies.

强制性的种间寄生是一种独特的寄生形式，一种蚂蚁从另一种蚂蚁那里窃取蛹，并将它们培养成工蚁，在巢中履行职责。虽然这种策略可以支持非常大的群体，但这些群居寄生虫的相对物种丰度总是很低。利用已被充分研究的胶木属掠巢虫与寄主之间相互作用的全参数化数学模型，我们旨在发现限制掠巢虫丰度的机制。这些数学模型解释了观察到的这些群居寄生虫相对物种丰度的范围，并为聚螨在一个寄主斑块内的持久性提供了一个标准。特别是，波利格斯蚁群的生存取决于距离它们巢穴23米到73米之间的寄主蚁群的数量——近到足以发动袭击，但远到足以在袭击中幸存。这一数字表明，水蛭丰度的上限小于群落的10%。此外，我们还量化了蜂群突袭对附近寄主群体造成的适应性成本，这些寄主群体可以通过不断消耗工蜂资源而有效地阉割。这些发现为理解社会寄生的生态限制、其在塑造蚂蚁群落动态中的作用及其与宿主防御策略进化的联系提供了一个机制框架。

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引用次数: 0